The formula to find the area of a regular nonagon is:
[tex]\begin{gathered} A=\frac{9\cdot s\cdot a}{2} \\ \text{ Where} \\ A\text{ is the area} \\ s\text{ is the length of anyone side} \\ a\text{ is the length of the apothem} \end{gathered}[/tex]We replace the know values on the above formula and solve for s.
[tex]\begin{gathered} A=783ft^2 \\ a=14.5ft \\ A=\frac{9\cdot s\cdot a}{2} \\ 783ft^2=\frac{9\cdot s\cdot14.5ft}{2} \\ 783ft^2=\frac{s\cdot130.5ft}{2} \\ \text{ Mutiply by 2 from both sides} \\ 783ft^2\cdot2=\frac{s\cdot130.5ft}{2}\cdot2 \\ 1566ft^2=s\cdot130.5ft \\ \text{ Divide by }130.5ft\text{ from both sides} \\ \frac{1566ft^2}{130.5ft}=\frac{s\cdot130.5ft}{130.5ft} \\ 12ft=s \end{gathered}[/tex]Therefore, the length of each side of the regular nonagon is 12 ft.
